Equilibrium selection in a nonlinear duopoly game with adaptive expectations

We analyze a nonlinear discrete time Cournot duopoly game, where players ha ve adaptive expectations. The evolution of expected outputs over time is ge nerated by the iteration of a noninvertible two-dimensional map. The long-r un behavior is characterized by multistability, that is, the presence of co existing stable consistent beliefs, which correspond to Nash equilibria in the quantity space. Hence, a problem of equilibrium selection arises and th e long run outcome strongly depends on the choice of the players' initial b eliefs. We analyze the basins of attraction and their qualitative changes a s the model parameters vary. We illustrate that the basins might be nonconn ected sets and reveal the mechanism which is responsible for this often-neg lected kind of complexity. The analysis of the global bifurcations which ca use qualitative changes in the topological structure of the basins is carri ed out by the method of critical curves. (C) 2001 Elsevier Science B.V. All rights reserved.